Problem: Solve for $x$ and $y$ using substitution. ${-4x+2y = 12}$ ${x = -y+9}$
Answer: Since $x$ has already been solved for, substitute $-y+9$ for $x$ in the first equation. ${-4}{(-y+9)}{+ 2y = 12}$ Simplify and solve for $y$ $4y-36 + 2y = 12$ $6y-36 = 12$ $6y-36{+36} = 12{+36}$ $6y = 48$ $\dfrac{6y}{{6}} = \dfrac{48}{{6}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {x = -y+9}\thinspace$ to find $x$ ${x = -}{(8)}{ + 9}$ $x = -8 + 9$ ${x = 1}$ You can also plug ${y = 8}$ into $\thinspace {-4x+2y = 12}\thinspace$ and get the same answer for $x$ : ${-4x + 2}{(8)}{= 12}$ ${x = 1}$